186
T. Stankovski
References
1. J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, The Kuramoto model: a
simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005)
2. S. Achuthan, C.C. Canavier, Phase-resetting curves determine synchronization, phase locking,
and clustering in networks of neural oscillators. J. Neurosci. 29(16), 5218–5233 (2009)
3. F.A. Azevedo, L.R. Carvalho, L.T. Grinberg, J.M. Farfel, R.E. Ferretti, R.E. Leite, W.J. Filho,
R. Lent, S. Herculano-Houzel, Equal numbers of neuronal and nonneuronal cells make the
human brain an isometrically scaled-up primate brain. J. Comparat. Neurol. 513(5), 532–541
(2009)
4. C. Bick, M. Goodfellow, C.R. Laing, E.A. Martens, Understanding the dynamics of biological
and neural oscillator networks through exact mean-field reductions: a review. J. Mathemat.
Neurosci. 10, 9 (2020)
5. M. Breakspear, S. Heitmann, A. Daffertshofer, Generative models of cortical oscillations:
neurobiological implications of the Kuramoto model. Front. Human Neurosci. 4, 190 (2010)
6. E.N. Brown, J. Moehlis, P. Holmes, On the phase reduction and response dynamics of neural
oscillator populations. Neur. Comp. 16(4), 673–715 (2004)
7. G. Buzsáki, A. Draguhn, Neuronal oscillations in cortical networks. Science 304, 1926–1929
(2004)
8. R.T. Canolty, E. Edwards, S.S. Dalal, M. Soltani, S.S. Nagarajan, H.E. Kirsch, M.S. Berger,
N.M. Barbaro, R.T. Knight, High gamma power is phase-locked to theta oscillations in human
neocortex. Science 313(5793), 1626–1628 (2006)
9. R.T. Canolty, R.T. Knight, The functional role of cross-frequency coupling. Trends Cognit.
Sci. 14(11), 506–515 (2010)
10. B. Ermentrout, Type I membranes, phase resetting curves, and synchrony. Neural Comput.
8(5), 979–1001 (1996)
11. B. Ermentrout, D. Saunders, Phase resetting and coupling of noisy neural oscillators. J. Comput.
Neurosci. 20(2), 179–190 (2006)
12. G.B. Ermentrout, B. Beverlin, T. Netoff, Phase response curves to measure ion channel effects
on neurons, in Phase Response Curves in Neuroscience (Springer, 2012), pp. 207–236
13. A.S. Etémé, C.B. Tabi, J.F.B. Ateba, H.P.F. Ekobena, A. Mohamadou, T.C. Kofane, Neuronal
firing and DNA dynamics in a neural network. J. Phys. Comms. 2(12), 125004 (2018)
14. K.J. Friston, Functional and effective connectivity: a review. Brain. Connect. 1(1), 13–36 (2011)
15. K.J. Friston, L. Harrison, W. Penny, Dynamic causal modelling. Neuroimage 19(4), 1273–1302
(2003)
16. R.F. Galán, G.B. Ermentrout, N.N. Urban, Efficient estimation of phase-resetting curves in real
neurons and its significance for neural-network modeling. Phys. Rev. Lett. 94, 158101 (2005).
https://doi.org/10.1103/PhysRevLett.94.158101
17. W. Gerstner, W.M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity
(Cambridge University Press, 2002)
18. W. Gerstner, R. Naud, How good are neuron models? Science 326(5951), 379–380 (2009)
19. Z. Hagos, T. Stankovski, J. Newman, T. Pereira, P.V.E. McClintock, A. Stefanovska, Synchronization transitions caused by time-varying coupling functions. Philoso. Trans. R. Soc. A
377(2160), 20190275 (2019)
20. H. Haken, Synergetics, An Introduction (Springer, Berlin, 1983)
21. R. Haseloff, I. Blasig, H.C. Bauer, H. Bauer, In search of the astrocytic factor (s) modulating blood-brain barrier functions in brain capillary endothelial cells in vitro. Cell. Molecul.
Neurobiol. 25(1), 25–39 (2005)
22. M.H. Hassoun et al., Fundamentals of Artificial Neural Networks (MIT Press, 1995)
23. Y. He, A. Evans, Graph theoretical modeling of brain connectivity. Current Opin. Neurol. 23(4),
341–350 (2010)
24. A.L. Hodgkin, A.F. Huxley, Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. J. Physiol. 116(4), 449–472 (1952)
T. Stankovski
References
1. J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, The Kuramoto model: a
simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005)
2. S. Achuthan, C.C. Canavier, Phase-resetting curves determine synchronization, phase locking,
and clustering in networks of neural oscillators. J. Neurosci. 29(16), 5218–5233 (2009)
3. F.A. Azevedo, L.R. Carvalho, L.T. Grinberg, J.M. Farfel, R.E. Ferretti, R.E. Leite, W.J. Filho,
R. Lent, S. Herculano-Houzel, Equal numbers of neuronal and nonneuronal cells make the
human brain an isometrically scaled-up primate brain. J. Comparat. Neurol. 513(5), 532–541
(2009)
4. C. Bick, M. Goodfellow, C.R. Laing, E.A. Martens, Understanding the dynamics of biological
and neural oscillator networks through exact mean-field reductions: a review. J. Mathemat.
Neurosci. 10, 9 (2020)
5. M. Breakspear, S. Heitmann, A. Daffertshofer, Generative models of cortical oscillations:
neurobiological implications of the Kuramoto model. Front. Human Neurosci. 4, 190 (2010)
6. E.N. Brown, J. Moehlis, P. Holmes, On the phase reduction and response dynamics of neural
oscillator populations. Neur. Comp. 16(4), 673–715 (2004)
7. G. Buzsáki, A. Draguhn, Neuronal oscillations in cortical networks. Science 304, 1926–1929
(2004)
8. R.T. Canolty, E. Edwards, S.S. Dalal, M. Soltani, S.S. Nagarajan, H.E. Kirsch, M.S. Berger,
N.M. Barbaro, R.T. Knight, High gamma power is phase-locked to theta oscillations in human
neocortex. Science 313(5793), 1626–1628 (2006)
9. R.T. Canolty, R.T. Knight, The functional role of cross-frequency coupling. Trends Cognit.
Sci. 14(11), 506–515 (2010)
10. B. Ermentrout, Type I membranes, phase resetting curves, and synchrony. Neural Comput.
8(5), 979–1001 (1996)
11. B. Ermentrout, D. Saunders, Phase resetting and coupling of noisy neural oscillators. J. Comput.
Neurosci. 20(2), 179–190 (2006)
12. G.B. Ermentrout, B. Beverlin, T. Netoff, Phase response curves to measure ion channel effects
on neurons, in Phase Response Curves in Neuroscience (Springer, 2012), pp. 207–236
13. A.S. Etémé, C.B. Tabi, J.F.B. Ateba, H.P.F. Ekobena, A. Mohamadou, T.C. Kofane, Neuronal
firing and DNA dynamics in a neural network. J. Phys. Comms. 2(12), 125004 (2018)
14. K.J. Friston, Functional and effective connectivity: a review. Brain. Connect. 1(1), 13–36 (2011)
15. K.J. Friston, L. Harrison, W. Penny, Dynamic causal modelling. Neuroimage 19(4), 1273–1302
(2003)
16. R.F. Galán, G.B. Ermentrout, N.N. Urban, Efficient estimation of phase-resetting curves in real
neurons and its significance for neural-network modeling. Phys. Rev. Lett. 94, 158101 (2005).
https://doi.org/10.1103/PhysRevLett.94.158101
17. W. Gerstner, W.M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity
(Cambridge University Press, 2002)
18. W. Gerstner, R. Naud, How good are neuron models? Science 326(5951), 379–380 (2009)
19. Z. Hagos, T. Stankovski, J. Newman, T. Pereira, P.V.E. McClintock, A. Stefanovska, Synchronization transitions caused by time-varying coupling functions. Philoso. Trans. R. Soc. A
377(2160), 20190275 (2019)
20. H. Haken, Synergetics, An Introduction (Springer, Berlin, 1983)
21. R. Haseloff, I. Blasig, H.C. Bauer, H. Bauer, In search of the astrocytic factor (s) modulating blood-brain barrier functions in brain capillary endothelial cells in vitro. Cell. Molecul.
Neurobiol. 25(1), 25–39 (2005)
22. M.H. Hassoun et al., Fundamentals of Artificial Neural Networks (MIT Press, 1995)
23. Y. He, A. Evans, Graph theoretical modeling of brain connectivity. Current Opin. Neurol. 23(4),
341–350 (2010)
24. A.L. Hodgkin, A.F. Huxley, Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. J. Physiol. 116(4), 449–472 (1952)